engineering mechanics question papers

8/18/2019 Engineering Mechanics QUESTION PAPERS

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ENGINEERING MECHANICS

First Year Group (A) DnyanPath Publication, Amravat

EnginEEr ing MECHAniCSUnit-I (EM)

(S-10)

Q. State different system of forces. 3

Q. Define couple. State its characteristics. 3

Q. Replace the system of force as shown in figure. into a single force

and couple about centre of circular plate. 7

OR

Q. State analytical and Graphical conditions of equilibrium. 3

Q. A 3.7m bar of negligible weight is loaded upon by a vertical load and

horizontal load as shown in figure. The end of the bar in contact with

a smooth vertical wall and smooth incline. Determine the equilibrium

position of the bar as defined as an angle `Ѳ` it makes with thehorizontal. 10

(W-10)

Q. (a) i) State and explain law of parallelogram of forces.

ii) Explain in different systems of forces.

iii) Define couple and state characteristic of a couple.

(b) A rigid T is made out of metal bars MN and PQ each 1.4m lo

and weight 4kN and 3kN respectively. It is suspended in

vertical plane. Compute angle for equilibrium subjected to

load of 500 N. Refer figure.

OR

Q. (a) i) state the condition of equilibrium for coplanar force system.

ii) Explain varignon’s theorem.

(b) A square ABCD has forces acting along its sides as shown in

figure. Find the values of P1 and P2 if the system reduces to a

couple. Also find magnitude of the couple, if the side of the

square is 2m.


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(c) Calculate support reactions for a compound beam as shown in

figure. 6

(S - 11)

Q. (a) Define :-

(i) Principle of physical independence of forces.

(ii) Principle of resolved parts of forces. 4

(b) A 500 N vertical force is applied to a 60cm long bar OA hinged

at O and inclined at 60⁰ to the horizontal. Determine:

(i) The moment of the 500N force about O.

(ii) The magnitude of the horizontal force `F` applied at A

which gives the same moment about O.

(iii) The smallest force applied at A which gives the same

moment about O.

(iv) At what distance from O, a vertical 1500 N force should

be applied which gives the same moment about O ? 10

OR

Q. (a) Prove that moment of couple at any point is same.

(b) Define:

(i) Varigonon`s theorem.(ii) Resolution of a force into force and a couple.

(c) Find support reactions of the beam shown in Fig.

(W - 11)

Q. (a) Explain the terms : (i) Resolution of force

(ii) Composition of forces.

(b) Find the resultant of the two forces shown in figure.

(c) Two forces acting on a body are 1500 N and 1000N as shown

fig.2. Determine the third force F such that the resultant of all

the three forces is 1000 N directed at 45⁰ to the +ve X axis. 6


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OR

Q. (a) Draw the Free Body diagram of various supports, 4

(b) The weights and radii of the three cylinders in a rectangular

ditch are as shown in fig. 3. Assuming all contact surfaces to besmooth, determine the reaction at all contact points of piled

cylinders A, B and C. 10

(S - 12)

Q. (a) (i) Define force and state its characteristics

(ii) Define couple and states its important significance

with example. 6

(b) Determine the magnitude, direction and position of the line of

action on the resultant the coplanar system of force shown in

fig.1 8

OR

Q. (a) (i) Define the term ‘Free Body Diagram (FBD)’ what is the

purpose of drawing FBD?

(ii) State and explain Lami`s theorem.

(b) In fig. 2 two cylinders, A of weight 4000 N and B of weight

2000 N, rest on smooth inclines. They are connected a bar of

negligible weight hinged to each cylinder at its geometric cent

by smooth pins Find the force P acting as shown that will hold

the system in the given position.

(W-12)

Q. (a) The following forces act at a point:

(i) 200 N inclined towards North of East,

(ii) 250 N toward North,


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(iii) 300 N towards North West, and

(iv) 350 N inclined at 40⁰ towards South of West.

Find the magnitude and direction of the resultant force.

Locate it in the force system itself. 5

(b) Two identical prism attic bars PQ and RS each weighing 75 N

are welded together to form a Tee and are suspended in a vertical

plane as shown in fig. 1. Calculate the value of ‘θ’ that the bar

PQ will make with vertical when load of 100 N is applied at S. 9

OR

Q. (a) Define the term ‘Free Body Diagram’. what is the purpose ofdrawing FBD? Draw the FBD of different types of supports used

in beam. 6

(b) Bar AB of negligible weight is subjected to a vertical force of

600 N and a horizontal force of 300 N applied as shown in fig. 2.

Find the angle θ at which equilibrium exist. Assume smooth

inclined. 8

(S - 13)

Q. (a)(i) Define Force. What is the various system of forces?(ii) State Principle of Transmissibility of Force.

(b) Determine the magnitude, direction and position of Resultant

Force about point ‘O’ for a given system.

OR

Q. (a) (i) State and explain Lami`s theorem.

(ii) State conditions of Equilibrium.

(b) Two smooth spheres of weigh 100 N and of radius 250mm ea

are in equilibrium in a horizontal channel of width 900 mm as

shown in fig. Find the reactions at surface of contact A,B,C an

D assuming all smooth surfaces.


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(W - 13)

Q (a) (i) Explain Resolutions and compositions of forces.

(ii) State and explain principle of transmissibility of forces. 6

(b) Determine the magnitude, direction and position of resultant

force about point p as shown in fig.1 (b) 8

OR

Q. (a) (i) State and derive Lami`s theorem. 6

(ii) State the conditions of equilibrium. 6

(b) Two rollers of weights p and Q are connected by flexible string

AB. The rollers rest on two mutually perpendicular planes DE

and EF as shown in fig. 2(b) find the tension in the string and

angle θ that it makes with the horizontal when the system is in

equilibrium Take p = 50N and Q = 100N. 8

(S - 14)

Q. (a) (i) State and explain law of parallelogram of forces.

(ii) Explain different systems of forces.

(iii) Define couple and state characteristics of a couple.

(iv) State principle of Transmissibility of force.

(b) A pole carrying electric wires is assumed to have no fo

bending it out of the vertical and has five horizontal wi

radiating from its tops. One extends due North, one 20⁰ North

East, one due South, one 15⁰ south of West, with tensions of 1

N, 180N, 145 N, and 200 N respectively. Find the direction

fifth wire and tension in it. The pole is in equilibrium Fo

acting on pole are coplanar concurrent.

OR

Q. (a) (i) Explain Varignon`s Theorem.

(ii) What is Free Body Diagram? Draw FBD of a weight `W`

placed on a horizontal surface.

(b) Calculate support reactions for a compound beam shown in

fig.2 (b).


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OR

Q. (a) (i) State principle of transmissibility of the force. 2

(ii) Define, `Resultant`. 2

(b) Determine components of forces P and F along X and Y axes

oriented parallel and perpendicular to the incline shown in

fig.1(b).(Force p is vertical and F is horizontal). 4

(c) Determine the resultant of the forces acting on the Fink truss

Shown in Fig.1(c) and its intersection on line AB. 6

OR

Q. (a) The forces at a joints of a truss are shown in Fig. 2(a).

Determine the value of P and F to maintain the equilibrium of

the joint.

(b) Determine the reactions at A and B for the truss shown in fig.1

(c).


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Unit-II (EM)

(S-10)

Q. State laws of static friction. 4

Q. A cylinder weighing 1KN rests in contact with two mutually

perpendicular walls as shown in figure. A horizontal force 250 N is

applied to the top of the cylinder will rotate or not. 9

Q. State assumptions made in Analysis of a truss. 4

Q. Analysis the truss as shown in figure. Tabulate the results. 9

(W-10)

Q. (a) (i) What is perfect truss and imperfect truss? 4

(ii) State the assumptions made in the analysis of plane truss. 2

(iii) State Coulomb`s laws of dry friction. 2

(b) Calculate the forces in the members of a truss as shown in

figure.

OR

Q. (a) Explain the terms :

(i) Angle of friction (ii) Cone of friction

(iii) Limiting friction (iv) Angle of repose

(b) Derive the expression for relationship between tight and slack

side of the belt.

(c) A horizontal weightless bar of 1.2m length resting on rough

inclines as shown in figure. If the angle of friction is 15⁰,

determine the minimum value of x at which Q = 250 N may be

applied before slipping impends.


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(S - 11)

Q. (a) State the assumptions made to simplify the analysis of the

truss. 3

(b) Determine the forces in the members of a truss shown in fig. 3(b)

which carries a horizontal load of 12kN and vertical load of18kN. 10

Q. (a) Prove angle of repose is equal to angle of friction. 3

(b) A rope making 1 ¼ turns around a stationary horizontal drum, is

used to support weight. If µ=0.3 what range of weight can be

supported by exerting a 600 N force at the other end of the rope?

4

(c) Determine the force P required to start the movement of wedge

as shown in fig. the angle of friction for all surfaces is 15⁰. 6

(W - 11)

Q (a) Explain method of section for ideally connected truss.

(b) Determine the ‘induced forces’ in each member of the truss as

loaded and supported as shown in fig.

OR

Q. (a) Prove that, angle of friction is always equal to angle of repose.

(b) A horizontal weightless bar of 1.2 m length resting on rou

inclines is shown in fig. 5 If the angle of friction is 1

determine the minimum value of `x` at which Q=250 N may

applied in-fore slipping impends.

(S - 12)

Q. (a) (i) State the assumptions made in the analysis of truss.

(ii) State the advantage of section method over the joint meth

in the analysis of truss.


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(b) Determine the forces in the various members of the structure

shown in fig.3 7

OR

Q. (a) Derive the relation between tension in light side and slack side

in belt friction. 5

(b) A uniform rod AB of length 2.5m weighing 500N is hinged at B,

with end A resting on a 750 N block which, in turn, rests on a

horizontal plane as shown in fig.4. The coefficient of friction at

all contact surfaces is 0.30. Determine the minimum value of

horizontal force p required to start right ward motion of the

block. 8

(W - 12)

Q (a) State the advantages of method of section over the method of

joint. 3

(b) Determine the magnitude and nature of forces in all the memb

of the truss shown in fig.3. Also tabulate the forces in the

members of a truss.

OR

Q. (a) Derive the relation between tension in tight side and tension in

slack side in belt friction.

(b) A uniform rod AB of length 205m weighing 500 N is hinges at

B, with A resting on a 1000 N block which in turn rests on a

horizontal plane as shown in fig - 4 Determine the minimum

value of horizontal force required to start rightward motion of

the block.


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First Year Group (A) DnyanPath Publication, Amravati

(S - 13)

Q. (a) Define Truss. State the assumptions made in the analysis of

truss. 5

(b) Find the forces in all the members of the truss shown in Fig.Tabulate the results. 8

OR

Q. (a) State the Coulomb`s law of dry friction. 4

(b) A weight of 20 kN is to be raised by means of a wedge. Find the

value of P for impending motion of block A. Angle of friction

for all contact surface is 15⁰. 9

(W - 13)

Q. (a) Explain with near sketches.

(i) Perfect truss. (ii) Imperfect truss.

(b) Find the forces in following members of truss as shown infig.3(b) AB,AD,BC,CF,BD,BF,DE and EF.

OR

Q. (a) Derive relation between tension in tight side and slack side in

belt friction.

(b) Block A and B shown in fig 4(b) weight 200 N and 300N

respectively. Find the least weight of block D to start in

moving.


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(S-14)

Q. (a) (i) Differentiate between a perfect and imperfect truss. 3

(ii) State the assumptions made in the analysis of truss. 3

(b) Determine the support reactions and forces in the members of

the truss shown in Fig.3 (b). 7

OR

Q. (a) (i) State the laws of friction. 3

(ii) Define coefficient of friction and limiting friction. 2

(iii) What is wedge? 1

(b) A ladder 5m long rests on a horizontal ground and leans against

a smooth vertical wall at an angle 70⁰ with the horizontal. The

mass of the ladder is 90 kg and acts at its middle. The ladder is at

the point of sliding, when a man of mass 75kg stands on a rung 3.5

from the top of the ladder. Calculate the coefficient of friction betwe

the ladder and the floor?

(W - 14)

Q. (a) Write any four assumptions made in analysis of simple trusses.

(b) Determine the force in each member of the truss shown in

Fig.3(b).

OR

Q. (a) Define :

(i) Angle of friction. (ii) Coefficient of friction.

(b) Determine the force `P` required to start the wedge shown in

Fig4 (b). The angle of friction is 15⁰ for all surfaces.


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(c) Write the relation between tension in tight side and slack side of

the belt if β is the angle of contact of the belt with the drum. 2

Unit-III (EM)

(S - 10)

Q. Locate the position of centroid for a semicircular plane lamina from

the fundamentals. The radius `R`. 5

Q. Determine Principal Moment of Inertia and Locate Principle axes for

the section as shown in figure. 9

(W - 10)

Q. i) What is the difference between centroid and center of gravity? 2

ii) What is the moment of inertia of triangle about the axis passing

through the base of a triangle and transfer it about a centroidal

axis parallel to base ? 2

(b) Find the moment of inertia of a plane area shown in figure about

horizontal and vertical axes passing through centroid. 9

OR

Q. (a) State and explain the principle of virtual work. What are the

advantages of this method when applied to connected system

of rigid bodies in equilibrium?

(b) Using method of virtual work find the beam reaction for a bealoaded as shown in figure.

(S-11)

Q. (a) Explain (i) Perpendicular axis theorem.(ii) Parallel axis theorem.

(b). Find moment of inertia of the shaded area shown in fig.5

about the axis AB. Also find radius of gyration with respect

AB axis. All dimensions shown in fig. are in mm.

OR

Q. (a) Explain work done by forces and moments with the help of ne

sketch.


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(b) Determine the reactions at A and B developed in the beam

shown in Fig. using principle of virtual work. 9

(W - 11)

Q. (a) State and explain perpendicular axis theorem. 4

(b) Determine the second moment of shaded area about centroidal

axes. (Ref. fig.) 9

OR

Q. (a) For the shaded area shown in fig.7 created by cutting a

semicircle of diameter R from a quarter circle of radius R. Find

product of inertia about base axes. 4

(b) A simply supported beam of span 5m carries point loads of 2

and 3 km at a distance 2m and 4m from left support respective

Find support reaction by using Virtual Work principle (Ref. fi

(S - 12)

Q. (a) Define the following terms :

(i) Centroid. (ii) Radius of Gyration.

(iii) Product of inertia. (iv) Principle moment of inertia.

(b) For the Z section determine :

(i) Moment of inertia about centroidal axis.

(ii) Product of inertia about centroidal axis.

OR

Q. (a) (i) State and prove parallel axis theorem.

(ii) State the principle of virtual work and explain how it can

used for solving problem in statics.


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(b) A simply supported beam AB of span 5m loaded as shown in fig.

6, by using principle of virtual work find reactions at supported

A and B. 5

(W - 12)

Q. (a) Give the steps involved in locating centroid of any plane

Lamina. 4

(b) For the shaded area shown in fig. 5 find:(i) centroid about given x and y axes.

(ii) Moment of inertia about both the axis. 9

OR

Q. (a) A simply supported beam AB of span 6m is loaded as shown in

fig. by using principle of virtual work. Find the reactions at

support A and B. 4

(b) Find the principle moment of inertia for the angle section sho

in fig 7.

(S - 13)

Q. (a) State and prove parallel axis theorem.

(b) For the shaded area as shown:

(1) Locate the position of centroid.

(2) Find out product of inertia about given x and y axis.


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OR

Q. (a) State and explain principle of Virtual work. 5

(b) Determine the support reactions at A and B for beam shown in

Fig. 8

(W - 13)

Q. (a) Derive the expression for moment of inertia of a triangle of

height h and base b about x-axis coinciding with the base. 5

(b) Locate the position of centroid and determine the product of

inertia with respect to given x and y axis of the shaded area as

shown in fig.5 (b) 8

OR

Q. (a) (i) State and prove parallel axis theorem.

(ii) State and explain principle of virtual work. 7

(b) Find reaction at support A and B use principle of virtual work.

(S - 14)

5. (a) (i) What is the difference between centroid and center of

gravity?

(ii) What is the moment of inertia of triangle about the axis

passing through the base of a triangle and transfer it abou

a centroidal axis parallel to base?

(b) Find the moment of inertia for the given I-section shown in fig

(b) about the principle axes.

OR

Q. (a) Define the following terms:

(i) Product of inertia. (ii) Principle moment of inertia.

(iii) Radius of Gyration.


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(b) A beam OA of length 1m and negligible weight is hinged at O

and has a load W at the midpoint of beam as shown in Fig.6 (b).

By the method of virtual work only find the tension in the wire.

8

(W - 14)

Q. (a) Locate the centroid of the figure 5(a) with respect to given X

and Y axes. The diameter of inner semicircle is 2 cm and outer

circle is 3 cm. 5

(b) Determine the Moment of Inertia about the centroidal X and Yaxes of the I section shown in Fig.5 (b). 8

OR

Q. (a) Determine Principle moment of Inertia of the fig.6(a).

(b) By principal of virtual work determine R A and R B of the simp

supported beam shown in Fig.6(b).

Unit-IV (EM)

(S - 10)

Q. A particle at the origin is starting from rest and is accelerated as giv

by the equation2

2a =

V + 1 were `a` acceleration in m/sec

2. Determi

the velocity when the displacement is 50m.

Q. A particle starting with an initial velocity of 1829 cm/sec has

rectilinear motion with a constant deceleration of 304.8 cm/se

Determine the velocity and displacement at the end of 9 sec by

sketching the a-t, v-t and s-t curve.


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Q. Power supply was cut off to power driven wheel when it was rotating

at a speed of 750 rpm. It was observed to come to rest after making

300 revolutions. Determine its angular retardation and time it took to

come to rest after power supply was cut off. 7

Q. The velocity of a particle is defined by3/ 2

100 xV t and2100 10 2 yV t t where V is in m/sec and t is in sec. determines the

radius of curvature at the top of its path. 7

(W - 10)

Q. (a) A stone is thrown vertically upward with a velocity of 20m/s

from 25m high tower top. Determine the

i) Time required for stone to reach the ground .

ii) Velocity of stone during downward movement at the level

of point of projection and

iii) Maximum height attained during flight. 7

(b) The acceleration of an object moving along a straight path

decrease uniformly from 10m/s2 to zero in 12 sec. at which its

final velocity is 6 m/s Find its initial velocity and change in its

position during 12 sec, inertial use motion curve method. 7

OR

Q. (a) Position co-ordinate of a particle is given by2 3ˆ ˆ ˆr = 6ti + 2t j + 1/6t k .Determine the tangential and normal

component of acceleration and principle radius of curvature at

t=2 second. 7

(b) A fly wheel of 550 mm diameter is brought uniformly from rest

upto a speed of 350 rpm in 20 sec. Find the velocity and the

acceleration of a point on its rim 3 sec after starting from rest. 7

(S-11)

Q (a) A body falling freely under the action of gravity passes two

points 15m apart vertically in).3 second from what height abo

the higher point did it start to fall?

(b) A particle starting from the origin is subjected to acceleration

such that a=-3 m/s2 and ay=11 m/s

2. If the initial velocity 80

is directed at a slope of 4:3, compute radius of curvature of t

path after 4 seconds.

OR

Q. (a) Define the two methods of locating Instantaneous centre.

(b) Find the velocity of B using instantaneous centre method for

beam A B shown in fig. 8 (b)

4

(c) Length of crank AB is 100 mm and that of connecting rod is 2

mm as shown in fig.8(c) if the crank AB is rotating in clockwdirection at 1500 r.p.m, for the position shown in fig. determ

the angular velocity of the connecting rod and the velocity of t

piston.


18/31



(W - 11)

Q. (a) Two ears A and B travelling in the same direction get stopped at

traffic signal. When the signal turns green, car A accelerate at

0.75 m/sec2. 1.75 second later, car B starts and accelerates at 1.1

m/sec2 Determine

(i) When and where B will overtake A,

(ii) The speed of each car at that time. 7

(b) A flywheel rotating freely at the speed of 1750 rpm clockwise to

provide with a counterclockwise torque, which is first applied at

time t=0 producing a counterclockwise 7

Acceleration, α=(4,5t) rad /sec2. Determine the

(i) Time required to produce clockwise angular speed 950rpm.

(ii) Time required to reverse direction of rotation.

(iii) Total number of revolution during first 14 sec. of

movement .

OR

Q. (a) Derive an expression for a range of projectile traversed by a

stone thrown with an initial velocity ‘U and an inclination of ‘α’

3

(b) Explain ‘motion curve’. What do you mean by s-t, v-t, and a-t

curve? 5

(c) Motion of a particle is defined by x - 7t and y = 4 - ft2 wher

and y are displacement along x and y axis respectively and t

time in seconds. Find normal tangential components

acceleration at t = 3 sec.

(S-12)

Q. (a) Define :

(i) Range of projectile (ii) Path of trajectory

(iii) Maximum height (iv) Angle of projection

(v) Time of Height (vi) Velocity of projection

(b) The rectilinear motion of a particle is governed by a = 8s-2 wh

is in m /sec2 and in meters when t = a sec, s = 4m and v

2m/sec. Determine displacement, velocity and the accelerationthe particle at t = 4 sec.

OR

Q. (a) A stone is thrown with an initial velocity of 30 m/sec upward

60 to the horizontal. Compute the radius of curve of its path at

the position where it is 15m horizontal form its initial position.

(b) A particle starting with an initial velocity of 1829 cm/sec harectilinear motion with a constant declaration of 304.8 cm/se

Determine the velocity and displacement at the end of 9 sec

sketching the a-t, v-t, s-t curves and using relations betwe

them.


19/31



(W - 12)

Q. (a) A train starting from rest is uniformly accelerated during the

first 250m of its run, after which it runs the next 750 m at the

uniform speed acquired. It is then brought to rest in 50 seconds,

under uniform retardation if the time of entire journey is 5minutes, find the acceleration with which the train started and

the retardation with which it stopped? Draw the motion curves.

8

(b) The retardation of a body starting from rest is given by the

equation a = 12-0.1S ; where, a is the retardation in m/sec and S

is the displacement in meters. Determine the velocity of the body

when a distance of 100m is covered and the distance at which

velocity will be zero again. 6

OR

Q. (a) A cricket ball thrown by a fielder from a height of 2m , at an

angle of 30⁰ to the horizontal with an initial velocity of 20 m/sec,

hits the wickets at a height of 0.5 m from the ground How far

was the fielder from the wickets? 6

(b) A wheel rotating about a fixed axis at 20 revolutions per minute

is uniformly accelerated for 70 second during which it makes 50

revolutions. Find the –

(i) Angular velocity at the end of his interval and

(ii) Time required for the velocity to reach 100 revolutions per

minute. 8

(S - 13)

Q. (a) A particle moves in x-y plane and position is given by-

2r =(3t)i + (4t - 3t ) j where r

is position vector of a particle in

meters and time t in second. Find radius of curvature of its path

and total acceleration when it crosses x-axis again. 7

(b) A bullet is fired from a height of 120 m at a velocity of 3

kmph at an angle of 30⁰ upwards. Neglecting air resistances

find :

(1) Horizontal range of the bullet

(2) Maximum height reache by bullet

(3) Find velocity of bullet just before touching the ground.

OR

Q. (a) The rectilinear motion of a particle is defined by a = 10 v1/2 .

an instant t=2 sec; 100m/s. Find displacement at t = 4 sec.

(b) The motion of a particle starting from rest is governed by a

curve shown in fig. sketch V-T and S-T curves. Determi

displacement at t = 9sec.

(W - 13)

Q. (a) Curved portion of the v-t curve as shown in fig.7(a) are second

degree parabolas with horizontal slope at t = 0 and t = 12 sec.

sketch a - t and s - t curve if S0 = 0. Calculate distance covered

18 seconds.


20/31



(b) A bullet is fired from top of tower 100 m high. With velocity 40

m/sec. at an angle of elevation 60⁰. Determine : 7

(1) The horizontal distance it will cover at the time it reaching

the ground.

(2) The magnitude and direction of velocity when it reaches

the ground.

(3) Maximum height reached by bullet.

OR

Q. (a) The rectilinear motion of a particle is governed by a=-8S-2

where a is in m/sec2 and S is in meter. When t=1sec; s = 4m and

v = 2m/sec. Determine acceleration of a particle at t= 2sec. 7

(b) A stone is thrown with an initial velocity of 30 m/sec. Upward at60⁰ to the horizontal compute the radius of curvature of its path

at the position where it is 15 m horizontally from it’s initial

position. 7

(S - 14)

Q. (a) A car starts from rest and reaches a speed of 15 m/sec in 15

seconds. The acceleration increases from zero uniformly with

time for the first 6 sec after which it remains constant. Compute

the distance travelled in 15 seconds. 6

(b) A shot is fired from a gun. After 2 second the resultant veloc

is inclined at 30˚up the horizontal. After one more second

resultant velocity is horizontal. Determine initial velocity a

angle of projection. Find also the radius of curvature at t=3s

OR

Q. (a) The rotation of a flywheel is governed by the equation ω= 6t

2t3/2 where ω is angular velocity in rad / sec and t is time in se

If the flywheel starts from rest, calculate its maximum angular

velocity and the displacement at that instant.

(b) A wheel of 1m diameter rolls freely without slipping. At

certain position ω = 3 rad/sec and α = 5 rad/sec2 both clockwi

Compute the velocity and acceleration of the point of the powhich is 0.3m from the centre of the wheel making an angle

30˚ anticlockwise with horizontal.

(W - 14)

Q. (a) Car A had a start with an acceleration of 2m/s2. Car B comes 5

sec after car A to chase Car A with a uniform velocity of 20m/

Find the time taken by Car B to overtake Car A.

(b) A particle has an initial velocity of 30m/sec up to the right at

with the horizontal. The components of acceleration are const

at ax=-1.2 m/s2 and ay=-6 m/s

2. Compute the horizontal dista

covered until the particle reaches a point 18 m below the point

projection.


21/31



OR

Q. (a) The curved portions of the v-t curve shown in fig. 8(a) are

second degree parabolas with horizontal slope at t= 0 sec and t =

12 sec. Sketch a-t and s-t curve if s₀ is zero. 9

(b) The rotation of a flywheel is governed by the relation = 10t - t2

where α is a rad/s

2

and t in sec. How many revolutions will thefly wheel make, starting from rest, before it momentarily stops

prior to reversing is direction. 5

Unit-V (EM)

(S - 10)

Q. State and explain D' Alemberts principle. 3

Q. In fig. 1 determine acceleration of Body A and the tension in the cord

attached to B. 10

Q. For the system shown in fig.2 determine the minimum weight

body C that will keep it at rest. For each incline, the coefficien

of friction is 0.25.

(W-10)

Q. (a) State D'Almbert principle.

(b) Two block shown in figure have masses A=8kg and B=4kg an

the coefficient of friction between the block A and the plane

µ=0.25

If the system is released, from rest and the block B falls throu

a vertical distance of 1m, what is velocity acquired by it at t

end of 1m distance? Neglect the friction in pulley and t

extension of the string.

OR

Q. (a) What is dynamic equilibrium ? State the equation of kinetics a

applied to a rigid bodies.

(b) The coefficient of dynamic friction is 0.25 under block A

shown in fig. Find the acceleration of each block and the angu

acceleration of compound pulley C.


22/31



(S - 11)

Q. (a) A small body B of 20N weight swings in horizontal plane as

shown in fig.9(a). Line BO is 50 cm long has a constant speed

in xz plane of 36 r.p.m. Determine the tension in the cord and

angle θ.

(b) A small particle of mass 3 kg slides down a curve path and pass

the lowest point with a speed of 3.6m/s. If the radius of curvature

at lowest point is 4m, determine the normal force exerted by the

path at this lowest point. 6

OR

Q. (a) The composite pulley shown in fig. 10(a) weights 800 N and has

a radius of gyration of 0.6. The 2000 N and 4000 N blocks are

attached to the pulley by strings, determine the tension in the

strings and angular acceleration of the pulley. 6

(b) Rod AB, weighing 200N is welded to the rod CD weighing 1

N as shown in fig. 10(b). The assembly is hinged at A and

freely held. Determine the instantaneous vertical and horizon

reactions of A when a horizontal force of 300 N acts at

distance of 0.75m from A.

(W - 11)

Q. (a) What do you understand by dynamic equilibrium? Explain

briefly.

(b) In fig.9, determine the acceleration of body A and B the tensi

in the cords attached to it (WA-300 N and WB = 400 N).

OR

Q. The pulleys in fig. are frictionless and of negligible weight Determi

acceleration of each block and tension in cable supporting blo

`C`(WA-400 N and WB =600 N,WC=300N).


23/31



(S - 12)

Q. (a) State and explain D`A Alembert`s principle. 3

(b) Two blocks A and B are released from rest on 30⁰ incline, when

they are 18 m a part. The coefficient of friction under the upper

block A is 0.2 and that under the lower block B is 0.4 as shown

in fig.7. In what time block a reaches the block B? After theytouch and move as a single unit, what will be contact force

between them? Weight of the block A and B 1000 N and 800 N

respectively. 10

OR

Q. (a) A man weighing W Newton entered a lift which moves with an

acceleration of `a` m/sec2 . Find the force exerted by the man on

the floor of lift when-

(i) Lift is moving downward

(ii) Lift is moving upward. 6

(b) Two blocks A and B, Weighting 400N and 300N respective

are connected by a rigid bar of negligible weight and move alo

the smooth surfaces shown fig.8. If they from rest at the giv

position, determine the acceleration of B at this instant.

(W - 12)

Q. (a) State the equations of kinetics (conditions of dynamicequilibrium ) for rectilinear and curvilinear translation.

(b) Two blocks A and B connected by massless rigid rod 2m lo

are constrained to slide (Block A on the floor and Block

against the wall) as shown in Fig.8. If the system starts from r

at the given position by applying force of 1000 N as sho

calculate the acceleration of the two blocks.

Assume the surfaces to be frictionless. Masses of blocks A and

are 200 kg and 150kg respectively.


24/31



OR

Q. (a) Determine the force p that will give the body in fig. 9, an

acceleration of 1 .96 m/sec2. The coefficient of kinetic is 02. 4

(b) The pulley assembly shown in fig.10 weighs 200N and has a

centroidal radius of gyration of 2m the blocks are attached to the

assembly by cord wrapped around the pulleys. Determine theacceleration of each body and the tension in each cord. 9

(S - 13)

Q. (a) State and explain D` Alembert principle. 4

(b) Determine the velocity of block B after A has moved 6m from

rest. Use D` Alembert principle. 9

OR

Q. (a) Determine the force P that will give the body an acceleration o

0.2gm/s2. The coefficient of kinetic friction is 0.2.

(b) The pulley assembly shown in fig. weight 150 N and

centroidal radius of gyration of 2m. The blocks are attached

the assembly by cord wrapped around the pulleys. Determine t

acceleration of each body and tension in each cord.


25/31



(W - 13)

Q. (a) State and explain D' Alembert's principle. 4

(b) Determine velocity of block B after block A has moved 6m

starting from rest. Use D' Alembert's principle. 9

OR

Q. (a) A man of mass 75 kg entered a lift During first 3 sec of motion

from rest the tension in the hoisting cable is 8300 N. Determine

reaction exerted by lift on man`s feet during this interval and

upward velocity at the end of 3 sec. If the total mass of lift

including mass of man is 750kg . 4

(b) A frictionless step pulley mounted at top of an incline supports

block A restrained to slide over the incline and a block B

hanging from it as shown in fig.10(b) If mass of block A is 3kg

and it should acceleration at 2m/sec2 up the incline, Determine

the mass of block B. 9

(S - 14)

Q. (a) State and explain D' Alembert's principle.

(b) A system of frictionless pulleys carrier two weights hung

inextensible cords as shown in fig.9(b). Find:

(i) The acceleration of the weights and the tension in the cor

(ii) The velocity and displacement of weight B after 5 seco

from start if the system is released from start if the system

released from rest.

OR

Q. (a) State the equations of kinetics (condition of dynamics

equilibrium ) for rectangular and curvilinear translation.

(b) A cylinder weighting 890 N is welded to the end of 445N b

The assembly is supported by a horizontal axis at A and

vertical cable as shown in fig. 10(b). Compute the reaction at

an instant after cutting the cable.


26/31



(W - 14)

Q. (a) State D’Alembert’s principle. 3

(b) Referring to fig. 9(b) compute the acceleration of body B and the

tension in the cord supporting body A. 10

OR

Q. The uniform crate shown in figure 10 weights 200 N. It is pulled up

the incline by a counter weight W of 400 N. Find the maximum and

minimum values of `d` so that the crate does not turn over as it slides

up the incline . 13

Unit-VI (EM)

(S - 10)

Q. Derive work energy equation from basic principle.

Q. Determine the constant force `P` that will give the system of bod

shown in figure.3a velocity of 2m/sec after moving 3m from rest.

Q. A golf ball is dropped from a height of 3m upon a concrete floor. T

coefficient of restitution is 0.98. Find the height to which the b

rebounds in the first second and third bounces.

Q. Direct central impact occurs between a 270 N body moving rightw

at 3m/sec and 150 N Body moving leftward at 5m/sec. If t

coefficient of restitution is e=0.6. Determine average impact force

a time of impact lasting 0.1 sec.


27/31



(W - 10)

Q. (a) Derive the work energy equation and impulse momentum

equation for a linear motion of a rigid body. 4

(b) A 10kg block moves on a rough horizontal floor and hitsvertically suspended 20 kg sphere with a velocity of 10m/sec as

shown in figure. Assume that coefficient of restitution for impact

between lock and sphere, e = 0.8 coefficient of friction between

block A and floor = 0.2 length of suspension string of sphere

=2m. Duration of impact=0.01 sec. Calculate

i) Impulsive force

ii) Maximum and minimum tension string.

iii) Final position of block A with reference to place of impact.

iv) Angular displacement of sphere from place of impact.

OR

Q. (a) Explain the coefficient of restitution with reference to plastic

impact, elastic impact and perfectly elastic impact between rigid

bodies. 3

(b) Determine the velocity of body A in figure after it has moved

4m, starting from rest. Assume pulleys to be frictions and of

negligible weight. Use work energy approach. 10

(S - 11)

Q. (a) Derive work energy equation for translation.

(b) A wagon weighing 500 kN starts from rest, runs 30 metres do

one percent grade and strikes the bumper post. If the rolli

resistance of the track is 5N/kN, find the velocity of the wag

when it strikes the post. If the bumper spring which compres

1 mm for every 15 kN determine by how much this spring

be compressed. 8

OR

Q. (a) State and derive impulse momentum equation

(b) A ball is dropped form a height of 1m on a smooth floor. The

height of first bounce is 0.81 m.

Determine : (i) coefficient of restitution.

(ii) expected height of second bounce.


28/31



(W - 11)

Q. (a) State and explain the types of mechanical energy. 4

(b) After the block in fig. 11, has moved 3m from rest, the constant,

force P is removed. Find the velocity of the block when it returns

to its initial position.

Q. (a) What do you understand by impulsive force? State impulsemomentum equation. 3

(b) Define the coefficient of restitution and state its value for

perfectly plastic body. 3

(c) Two discs A and B weighting 200 N and 300 N respectively

approach each other with velocity 4m/sec and 2m/sec

respectively. If the Coefficient of Restitution is 0.6, find

(i) Their velocities after impact.

(ii) Loss of energy during impact.

(iii) If impact lasts for 0.01 sec. Find average impact force. 7

(S - 12)

Q. (a) State whether any works is done by a man pushing against a car

which does not move explain. 3

(b) In what distance will body A of fig. 9 attain a velocity of 3m/s

starting from rest. (WA=2000N & WB = 1500N). 10

OR

Q. (a) Derive linear impulse momentum equation.

(b) A bullet weight 0.5 N and moving with velocity of 400m/sec h

centrally a 30 N block of wood moving away at 15m/sec a

gets embedded in it. Find the velocity of the bullet after t

impact and the amount of kinetic energy lost.

(c) A ball is dropped from a height of 1m on a smooth floor. Theight of first bounce is 0.810 m. Determine :

(i) Coefficient of Restitution.

(ii) Expected height of second bounce.


29/31



(W - 12)

Q. (a) state and prove work energy equation for translation motion. 4

(b) A 2500 N block starting from rest as shown in fig. 11 slides

down at 60⁰ incline. After moving 1.5m it strikes a spring whose

modulus is 25 N/mm. If the coefficient of friction between the

block and the incline is 0.2, determine the maximum

deformation of the spring and the maximum velocity of the

block. 9

OR

Q. (a) Define the following terms:

(i) Line of impact. (ii) Direct impact.

(iii) Central impact. (iv) Eccentric impact.

(v) Coefficient of Restitution. 5(b) Two discs A and B weighing 200N and 300 N respectively

approach each other with velocities 4m/sec and 2m/sec

respectively. If the coefficient of restitution is 0.6 find;

(i) Their velocities just after impact.

(ii) Loss of energy during impact.

(iii) If the impact lasts for 0.01 sec, find average impact force.

8

(S - 13)

Q. (a) Derive Work-Energy Equation.

(b) A 600 N block slides down an incline having a slope o

vertical to 3 horizontal. It starts from rest and after moving 1.

strikes a spring whose stiffness is 4kN/m. If the coefficient

friction is 0.20. Determine maximum deformation of the spri

and maximum velocity of the block .

OR

Q. (a) A ball of weight 20N is dropped from a height of 7m, it

renounce to a height of 4m. Determine the linear impulse.

(b) A 50 N block A has velocity of 3m/sec when it strikes a 10

ball B suspended from 1.8m cord. If e=0.8, Determine the fi

position of block A.

(W - 13)

Q. (a) After the block as shown in fig.11(a) has moved 3m from rest

the constant force P=120N is removed. Final the velocity of th

block when it returns to its initial position Take µ=0.2.


30/31



Q. (b) A wagon weighing 600kN starts from rest, runs 30m down one

percent grade and strikes the bumper post. If the rolling

resistance of the track is 5 N/KN, find the velocity of the wagon

when it strikes the post the post. If the bumper spring which

compresses 1mm for every 15kN determine by how much this

spring will be compressed. 7

OR

Q. (a) A bullet weighing 0.5N and moving at 650m/s penetrates the

60N body in fig. 12(a) and emerges with a velocity of 180m/s.

How far and how long does the body then move? 6

(b) The system shown in fig.12(b) is moving rightward at a velocity

o 4.5m/s. When a constant horizontal force P is applied as

shown. Determine the value P that will give the system a

leftward velocity of 9m/s in a time interval of 12 sec. 7

(S - 14)

Q. (a) (i) Explain the coefficient of restitution with reference to plastic

impact, elastic impact and perfectly elastic impact between rigid

bodies. 3

(ii) A ball dropped from a height of 1600 mm is observed to

rebound to the height of 1100 mm from the horizontal floor.

Determine the coefficient of restitution.

(b) A pile hammer weighting 4500N falls freely through a height

2 m on to the pole top and drives a pile into ground by 15cCalculate the average resistance offered by soil and the amo

of energy lost at the impact if pile weighs 7500N and if the p

and hammer move together after impact.

OR

Q. (a) Derive the work energy equation and impulse momentum

equation for rectilinear translation.

(b) Determine the velocity of body A in fig.12(b) after it has move 4m starting from rest. Assume pulleys to be frictionless and

negligible weight. Use work energy approach.


31/31



(W - 14)

Q. (a) Derive work energy equation for translation. 3

(b) As shown in fig. 11(b), a 100 N body moves along the whoinclines for which the coefficient of µ=0.20 friction If the body

starts from rest at A and slides 60m down the 30⁰ incline, how

far will it then move along the other incline? 6

(c) An 800 N man, moving with a velocity of 3m/s jumps into a

3200 N boat. Determine the velocity of the boat after the jump if

its initial velocity is zero. 4

OR

Q. (a) A 600 N block slides down an incline having slope of 4 vertical

to 3 horizontal. It starts from rest and after moving 1.8m, strikes

a spring whose stiffness k = 4000 N/m. If coefficient of friction

µ = 0.20, determine the maximum deformation of the spring. 6

(b) A bullet weighing 0.5N and moving horizontally at 700m/sec

penetrates a 10N body resting on horizontal surface with

coefficient of friction µ=0.40 and emerges with a velocity of 220

m/s. How far and long the body?

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